Steven W. answered • 08/07/16
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Hi Fikri!
One convenient aspect of calculations with gravity is that, because gravity is conservative, the changes in gravitational potential energy depend only on the change in height, and not the path the object took to traverse that change in height. So all we have to know to compute the change in gravitational potential energy is the weight of the object, and the change in height it undergoes, since:
PEg = mgh
where
mg = weight (force of gravity on the object)
h = change in height object moves through
To deal with the problem as written, we would have to assume the object moves all the way up the slope. Otherwise, we cannot figure out the change in height. But, with that assumption, we can figure out the change in height.
Think of the incline as a right triangle, with the box moving fully along the 12 m hypotenuse, with the height being the side opposite the 30-degree angle of the incline. We need to compute the length of that side opposite, which is the height h, knowing the hypotenuse is 12 m and the angle is 30o. The relationship between those three quantities is described trigonometrically as:
sin(30o) = h/(12 m)
Using this, you can solve for h. Then the gravitational potential energy the object gains as it moves that distance up the incline is PEg = mgh.
This is a classic case where, for a particular question, the problem gives you more information that you need, since the magnitude and orientation of the force pulling the box up the incline is not needed to figure the change in gravitational potential energy (which ONLY depends on weight and change in height, not path taken to change the height).
If you would like to check a result, or have any other questions, just let me know!
